The greenhouse gas emission cuts being pledged by the world’s nations will fall short of restricting global warming to 2C, the UN’s climate chief and UK government sources have warned.

A rise beyond 2C, the internationally agreed safety limit, may push the climate beyond tipping points and into dangerous instability. The expected pledges are likely to limit temperature rises to about 3C.

But those negotiating towards a global agreement due to be settled in Paris in December remain upbeat. The current pledges would avoid a catastrophic rise of 5C that would ensue if no emissions cuts were made, and the agreement is expected to contain measures to ratchet up emissions cuts in future years.

Nonetheless, significant disagreements remain to be overcome, including how much money poor nations will receive to cope with warming and how any deal is policed.

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The UN’s climate chief, Christiana Figueres, said that so far 62 countries had submitted promises of emissions cuts ahead of the Paris meeting, covering about 70% of global emissions. UK government sources told the Guardian that pledges, called Intended Nationally Determined Contributions (INDCs), were expected from India, Brazil, Indonesia and other nations before Paris.

In total, all these pledges would cover 85% of global emissions, according to the source, but the cuts would fall short of those needed to restrict warming to 2C. Figueres said pledged cuts would only limit warming to 3C, while the UK source said about 2.5C, but stressed that these numbers are hard to predict precisely.

“What the INDCs will do is mark a very substantial departure from business as usual,” Figueres said. But she added: “Is 3C acceptable? No.”

Achieving the further carbon cuts needed to curb warming from 3C to 2C will depend on agreeing a deal in Paris that includes tough five-yearly reviews. That will be challenging but the prospects for a deal are good, according to the UK source. “The political conditions are there to do a deal, so we should do a deal,” he said. “It will not be a perfect deal, but it will be a big step.”

A key difference from the perceived failure of the UN climate summit in Copenhagen in 2009 is that the proposed Paris deal takes commitments made by each country and then feeds them into the global deal, rather than attempting the near impossible task of agreeing a strict global deal that then dictates what individual nations can do.

But this “bottom-up” approach means ambitious nations have to put political pressure on laggards. “If countries ‘lowball’ and put in something very weak, they have to justify that to their own public opinion and world opinion,” said the UK source. “In the end, you are not going to invade countries, you want to expose them to public scrutiny.”

The debate on one crucial aspect, climate aid, will move a step forward on 9 October at a meeting of the World Bank Group and the International Monetary Fund in Lima, Peru.

Developed nations have promised to “mobilise” $100bn a year to poorer nations by 2020 and the meeting will release an analysis of how much of that is already flowing via existing overseas aid programmes. The UK gave £930m in 2014, according to the UK source.

“We are going to get an agreement and it will have all the major countries in it, which did not look likely a few years ago,” said Nick Mabey, an expert on climate change negotiations and chief executive of green non-profit organisation E3G. “It is not going to deliver 2C overnight, but it will put in place immediate action and reduce warming.”

He said the world had changed a great deal since the Copenhagen summit in 2009, with many nations including China and the US now having concrete climate policies in place and with a thriving green economy worth trillions of dollars and driving down costs. “Everybody has more to lose from climate change than from a low carbon economy,” he said.